论文标题
放松的Mumford-Shah颜色和多相图像分割的各向异性和各向同性总变化的加权差异
A Weighted Difference of Anisotropic and Isotropic Total Variation for Relaxed Mumford-Shah Color and Multiphase Image Segmentation
论文作者
论文摘要
在一类分段构图像分割模型中，我们建议将各向异性和各向同性总变化（AITV）的加权差异合并，以使图像中的分区边界正规化。特别是，我们替换了拟议的AITV中Chan-Vese分割模型和模糊区域竞争模型中的总变异正则化。为了处理AITV的非凸性性质，我们应用了Convex算法（DCA），其中可以通过LinesEarch使用Primal Dual Hybrid渐变方法将子问题最小化。分析了DCA方案的收敛性。另外，讨论了对彩色图像分割的概括。在数值实验中，我们将所提出的模型与经典凸方法和各种图像上的两阶段分割方法（平滑然后进行阈值）进行了比较，这表明我们的模型在图像分割方面有效，并且相对于冲动噪声有鲁棒。
In a class of piecewise-constant image segmentation models, we propose to incorporate a weighted difference of anisotropic and isotropic total variation (AITV) to regularize the partition boundaries in an image. In particular, we replace the total variation regularization in the Chan-Vese segmentation model and a fuzzy region competition model by the proposed AITV. To deal with the nonconvex nature of AITV, we apply the difference-of-convex algorithm (DCA), in which the subproblems can be minimized by the primal-dual hybrid gradient method with linesearch. The convergence of the DCA scheme is analyzed. In addition, a generalization to color image segmentation is discussed. In the numerical experiments, we compare the proposed models with the classic convex approaches and the two-stage segmentation methods (smoothing and then thresholding) on various images, showing that our models are effective in image segmentation and robust with respect to impulsive noises.
